Is there any phrase where corporate means "shared by all" rather than "of corporation"?

As Hot Licks commented, this is a case where the meaning of a word has shifted over time, so that the "shared" definition rarely occurs anymore. However, it is still possible to use the word corporate in the "shared by the group" sense, if your context makes it clear that there is no corporation involved. The actual example given by Oxford dictionaries does this:

The service emphasizes the corporate responsibility of the congregation.

Here, because the example mentions "the congregation", it's clear that "corporate" cannot possibly refer to an abstract legal entity, so it must refer to the members of the congregation instead.

(Since it's mostly pointless to fight the tides of language evolution, as Ryan Rich said in his answer, you're probably better off just using "shared responsibility" in modern writing.)

There is an example of that usage given by Oxford:

The service emphasizes the corporate responsibility of the congregation.

In this sentence, 'corporate' can be replaced by 'shared' to prevent confusion with the more common usage of corporate (i.e. relating to a legal corporation).